Braised Fingerling Potatoes

Clean potatoes under running water; transfer to a medium saucepan with enough water to cover. Season with salt and pepper and add thyme and leek trimmings. Bring to a boil over high heat; immediately reduce to a simmer and cook until potatoes are easily pierced with the tip of a sharp knife, about 15 minutes. Remove from heat and keep potatoes warm in their liquid until ready to serve; drain before serving.